The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X X^2  1  1  1  1  1  1  X  0  X X^2  X  X  1  1  1  1  X  X  0 X^2  X  X X^2  0  1  X  X  1 X^2  X  X  0 X^2  0 X^2  1
 0  X X^2 X^2+X  0 X^2+X X^2  X  0 X^2+X X^2  X  0 X^2+X X^2  X  0 X^2+X  X X^2+X  X  X X^2  X  0 X^2 X^2+X  X X^2+X  X  X  X  0 X^2  0 X^2 X^2+X  X X^2+X  X  X  X  0 X^2 X^2 X^2  0 X^2  0 X^2+X  0 X^2+X  X  X X^2 X^2  X  0

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+22x^59+2x^60+4x^62+2x^63+1x^64

The gray image is a linear code over GF(2) with n=232, k=5 and d=118.
As d=119 is an upper bound for linear (232,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0725 seconds.